Other tags that relate to Starfish Spotting
Investigations. Generalising. Trial and improvement. Multiplication & division. Factors and multiples. Combinations. Games. Comparing and Ordering numbers. Working systematically. Addition & subtraction.There are 92 results
Broad Topics > Thinking Mathematically > Generalising
Sums and Differences 2
Age 7 to 11 Challenge Level:
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
The Add and Take-away Path
Age 5 to 7 Challenge Level:
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Build it up More
Age 7 to 11 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions!
Sums and Differences 1
Age 7 to 11 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Calendar Calculations
Age 7 to 11 Challenge Level:
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Journeys in Numberland
Age 7 to 11 Challenge Level:
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Magic Constants
Age 7 to 11 Challenge Level:
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Sitting Round the Party Tables
Age 5 to 11 Challenge Level:
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Unit Differences
Age 5 to 7 Challenge Level:
This challenge is about finding the difference between numbers which have the same tens digit.
Doplication
Age 7 to 11 Challenge Level:
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Broken Toaster
Age 7 to 11 Short Challenge Level:
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Magic Circles
Age 7 to 11 Challenge Level:
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Button-up Some More
Age 7 to 11 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Domino Numbers
Age 7 to 11 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Build it Up
Age 7 to 11 Challenge Level:
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Always, Sometimes or Never? KS1
Age 5 to 7 Challenge Level:
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Lots of Lollies
Age 5 to 7 Challenge Level:
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Number Differences
Age 7 to 11 Challenge Level:
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Strike it Out
Age 5 to 11 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Centred Squares
Age 7 to 11 Challenge Level:
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Tiling
Age 7 to 11 Challenge Level:
An investigation that gives you the opportunity to make and justify predictions.
Number Tracks
Age 7 to 11 Challenge Level:
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
How Odd
Age 5 to 7 Challenge Level:
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Area and Perimeter
Age 7 to 11 Challenge Level:
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Digit Addition
Age 5 to 11 Challenge Level:
Try out this number trick. What happens with different starting numbers? What do you notice?
Magic Vs
Age 7 to 11 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Unexpected Ordering
Age 5 to 7 Challenge Level:
Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?
Bundles of Cubes
Age 7 to 11 Challenge Level:
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Oddly
Age 7 to 11 Challenge Level:
Find the sum of all three-digit numbers each of whose digits is odd.
Strike it Out for Two
Age 5 to 11 Challenge Level:
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Growing Garlic
Age 5 to 7 Challenge Level:
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Dice Stairs
Age 7 to 11 Challenge Level:
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Move a Match
Age 7 to 11 Challenge Level:
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Stop the Clock
Age 5 to 7 Challenge Level:
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
More Numbers in the Ring
Age 5 to 7 Challenge Level:
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Surprising Split
Age 7 to 11 Challenge Level:
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
Truth or Lie
Age 7 to 11 Challenge Level:
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Simple Train Journeys
Age 5 to 11 Challenge Level:
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Break it Up!
Age 5 to 11 Challenge Level:
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Charitable Pennies
Age 7 to 14 Challenge Level:
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Round the Three Dice
Age 7 to 11 Challenge Level:
What happens when you round these three-digit numbers to the nearest 100?
The Great Tiling Count
Age 7 to 11 Challenge Level:
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Round and Round the Circle
Age 7 to 11 Challenge Level:
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Sticky Triangles
Age 7 to 11 Challenge Level:
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Lost Books
Age 7 to 11 Challenge Level:
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Polygonals
Age 7 to 11 Challenge Level:
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Stop the Clock for Two
Age 5 to 7 Challenge Level:
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Division Rules
Age 7 to 11 Challenge Level:
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Play to 37
Age 7 to 11 Challenge Level:
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
NRICH is part of the family of activities in the Millennium Mathematics Project.